Precalculus Examples

Let $f (x) = 3 x - 6$ and $g (x) = x - 2$ Find $\frac{f}{g}$ and its domain.

Step 1

Evaluate the numerator in $\frac{f}{g}$ .

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Step 1.1

Replace the function designators in $f$ with the actual functions.

$3 x - 6$

Step 1.2

Remove parentheses.

$3 x - 6$

Step 2

Evaluate the denominator in $\frac{f}{g}$ .

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Step 2.1

Replace the function designators in $g$ with the actual functions.

$x - 2$

Step 2.2

Remove parentheses.

$x - 2$

Step 3

Rewrite $\frac{f}{g}$ .

$\frac{3 x - 6}{x - 2}$

Step 4

Simplify $\frac{3 x - 6}{x - 2}$ .

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Step 4.1

Factor $3$ out of $3 x - 6$ .

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Step 4.1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 6}{x - 2}$

Step 4.1.2

Factor $3$ out of $- 6$ .

$\frac{3 x + 3 \cdot - 2}{x - 2}$

Step 4.1.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{3 (x - 2)}{x - 2}$

Step 4.2

Cancel the common factor of $x - 2$ .

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Step 4.2.1

Cancel the common factor.

$\frac{3 (x - 2)}{x - 2}$

Step 4.2.2

Divide $3$ by $1$ .

$3$